#1642 ⟨a, b | aab=ba, bba=a⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a³ = a and a ⋅ 1 = a, however a³ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = a and 1 ⋅ a = a, however b² ≠ 1

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

# ab:aab=ba,bba=a a/b - -
aaaa=a
ab=baa
bba=a

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

17 total

Σ	#	Presentation	Mapping
9	2065	⟨a, b \| aab=b, abba=b⟩	φ(a) = b, φ(b) = a
10	5176	⟨a, b \| aab=ba, baab=a⟩	φ(a) = a, φ(b) = b
11	12251	⟨a, b \| aaab=ab, abba=b⟩	φ(a) = b, φ(b) = a
11	12385	⟨a, b \| aaba=ba, abba=b⟩	φ(a) = b, φ(b) = a
11	12440	⟨a, b \| aabb=aa, baab=a⟩	φ(a) = a, φ(b) = b
11	12558	⟨a, b \| abba=aa, baab=a⟩	φ(a) = a, φ(b) = b
11	14854	⟨a, b \| abba=b, ababb=b⟩	φ(a) = b, φ(b) = a
11	14866	⟨a, b \| abba=b, babab=b⟩	φ(a) = b, φ(b) = a
11	15683	⟨a, b \| aab=ba, aabab=a⟩	φ(a) = a, φ(b) = b
11	15693	⟨a, b \| aab=ba, ababa=a⟩	φ(a) = a, φ(b) = b
11	15713	⟨a, b \| aab=ba, babaa=a⟩	φ(a) = a, φ(b) = b
11	18973	⟨a, b \| aab=b, aaabba=b⟩	φ(a) = b, φ(b) = a
11	18997	⟨a, b \| aab=b, abaaba=b⟩	φ(a) = b, φ(b) = a
11	19529	⟨a, b \| aab=b, aabba=ab⟩	φ(a) = b, φ(b) = a
11	19577	⟨a, b \| aab=b, baaba=ab⟩	φ(a) = b, φ(b) = a
11	20062	⟨a, b \| aab=b, aaab=bba⟩	φ(a) = b, φ(b) = a
11	20097	⟨a, b \| aab=b, abba=aab⟩	φ(a) = b, φ(b) = a